Ponder This

December 2016

The European Union's General Data Protection Regulation (GDPR) is bolstering privacy protection in general and for biometric features in particular.
We would like to hold a competition, but to make it fair we'd like to have all the participants be of similar strength.
Let's assume (for the sake of the challenge) that all the men can apply exactly the same force in a rope-pulling contest, and all the women can apply a different force, but again, same for all.
We want to make sure that all the participants have the same gender.
The simple way to do that (asking for gender in the application form) is not an option (since it might be regarded as a biometric feature), so instead we use a rope-pulling contest.
We have time for four such contests, where we can chose any two equal-sized disjoint subsets of participants and let them compete. If any of these four contests ends not in a tie (i.e., one group wins) then, of course, we've proved that our group is not mono-gender.
We need to find four contests that can prove that all the N participants have the same gender.
For example, here is such a solution for a group of N=16 people:
A ; B
A B ; C D
A B C D ; E F G H
A B C D E F G H ; I J K L M N O P
The challenge, this month, is to find a solution for N at least 27. Bonus '*' for bigger Ns. Use "ABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789" to mark the participants.